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EE 435 Lect 23 Spring 2010

# EE 435 Lect 23 Spring 2010 - EE 435 Lecture 23 Common-Mode...

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Offset Voltage V OS Can be modeled as a dc voltage source in series with the input .• • • Review from last lecture .•
Random Offset Voltages OS 2 p 22 VTO n n VTO p V 2 n n p A μ L σ 2+ A W L μ ⎡⎤ ⎢⎥ ⎣⎦ + + + + + + + + μ μ + = σ μ μ 2 p p 2 n n 2 w 2 p p 2 n n 2 L p p n n 2 COX 2 p p 2 n n 2 EBn 2 VTOp 2 p n n n p n n 2 VTOn 2 V W L 1 W L 1 A L W 1 L W 1 A 2 L W 1 L W 1 A A L W 1 A L W 1 4 V A L W L L W A 2 p n OS M 1 M 2 M 3 M 4 V DD V 1 V 2 V X V S I T V OUT Correspondingly: which again simplifies to Note these offset voltage expressions are identical! .• • • Review from last lecture .•

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Random Offset Voltages 2 2 2 Jp 2 Jn t En Ep A A 2V + AA OS V σ ± Jn Jp A = A = 0.1 μ where very approximately It can be shown that .• • • Review from last lecture .•
Random Offset Voltages Typical offset voltages: MOS - 5mV to 50MV BJT - 0.5mV to 5mV These can be scaled with extreme device dimensions Often more practical to include offset-compensation circuitry .• • • Review from last lecture .•

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Common Centroid Layouts Almost Theorem: Define p to be a process parameter that varies with lateral position throughout the region defined by the channel of the transistor. If p(x,y) varies linearly throughout a two-dimensional region, then Parameters such at V T , μ and C OX vary throughout a two-dimensional region If a parameter varies linearly throughout a two-dimensional region, it is said to have a linear gradient. () = A EQ dxdy y x, p A 1 p .• • • Review from last lecture .•
Common Centroid Layouts Almost Theorem: If p(x,y) varies linearly throughout a two-dimensional region, then p EQ =p(x 0 .y 0 ) where x 0 ,y 0 is the geometric centroid to the region. Parameters such at V T , μ and C OX vary throughout a two-dimensional region If a parameter varies linearly throughout a two-dimensional region, it is said to have a linear gradient. Many parameters have a dominantly linear gradient over rather small regions .• • • Review from last lecture .•

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(x 0 ,y 0 ) () = A EQ dxdy y x, p A 1 p If ρ (x,y) varies linearly in any direction, then the theorem states () () EQ 0 0 A 1 p p x,y dxdy p x ,y A == (x 0 ,y 0 ) is geometric centroid .• • • Review from last lecture .•
Common Centroid Layouts Almost Theorem: A layout of two devices is termed a common-centroid layout if both devices have the same geometric centroid If p(x,y) varies linearly throughout a two-dimensional region, then if two have the same centroid, the parameters are matched !

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EE 435 Lect 23 Spring 2010 - EE 435 Lecture 23 Common-Mode...

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